This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
in this paper the second order neutral differential equations are incestigated are were we give some new suffucient conditions for all nonoscillatory
An optical system including quantum dot cylindrical Fresnel lens (CFL) has been designed by using Zemax optical designing program. Quantum dot cylindrical Fresnel lens has a relatively small thickness compared to conventional lenses and high absorbance. It contains grooves in the form of parallel lines, and each groove represents an individual lens that works to change the path of light falling on it to a single focal line. (CFL) is characterized by its small focal length despite its large area and small thickness, due to the nature of its design that gives this feature, which is applied in many optical systems (imaging and non- imaging system). In this paper, the visual properties of the (CFL) were studied as it is one of the impor
... Show MoreOne of the major problems in modern construction is the accumulation of construction and demolition waste; this study thus examines the consumption of waste brick in concrete based on the use of blended nano brick powder as replacement for cement and as a fine aggregate. Seven concrete mixes were developed according to ACI 211.1 using recycled waste brick. Nano powder brick at 0, 5, and 10% was used as a replacement by cement weight, with other mixes featuring 10, 20, and 30% partial replacement by volume of river sand with brick. The experimental results for replacement of cement with nano brick powder showed an enhancement in mechanical properties (compressive, flexural, and tensile strength) at 7,
The research aims to investigate the effects of GMAW or MIG welding process on the mechanical properties of dissimilar aluminum alloys 2024-T351 and AA 6061- T651. A series of experimental techniques have been conducted to evaluate mechanical properties of the alloys, by carrying out hardness, tensile and bending tests for welded and un-welded specimens.
Metal inert gas (MIG) has been carried out on sheet metal using ER- 4043(AlSi5) as a filler metal and argon as shielded gas. The welded joints were tested by X-ray radiography and Faulty pieces were excluded.
Welding joints without defects are subjected to heat treatment including heating the joints in furnace to 170 °C for half an hour then air cooling to rel
... Show MoreThe optical energy gap and optical constants such as the reflective index, dielectric constant have been evaluated due to The optical transmission and UV-VIS absorption spectra have been recorded in the wavelength (200 - 1100 nm) for PVA/PANI polymer blends and PVA/PANI/ZnO nanocomposites with different concentrations of ZnO (0.02, 0.05, 0.07, 0.1and 0.2) wt %. The results indicate that the materials have allowed direct transition. The reflection index and dielectric constant are increase with wavelength
In this paper, a study was made to determine the properties of Jovian radio bursts emitted at frequency 20.1MHZ. The data were provided from the Radio Jove archive for twelve years (2000-2012) for multi stations. The duration time for Long bursts (L) was (10-30) seconds and for Short bursts (S) was (10-20) seconds. The effect of radio bursts from the Sun and the galactic background were calculated at the same frequency and were found that radio bursts from the Sun will reduce the occurrence probability of Jovian radio bursts much more than radio bursts from the galactic background. The distribution of Jovian radio bursts was different; the occurrence probability with respect to the northern latitudes was more than the southern latitudes.
The aim of this research is to study the surface alteration characteristics and surface morphology of the superhydrophobic/hydrophobic nanocomposite coatings prepared by an electrospinning method to coat various materials such as glass and metal. This is considered as a low cost method of fabrication for polymer solutions of Polystyrene (PS), Polymethylmethacrylate (PMMA) and Silicone Rubber (RTV). Si were prepared in various wt% of composition for each solutions. Contact angle measurement, surface tension, viscosity, roughness tests were calculated for all specimens. SEM showed the morphology of the surfaces after coated. PS and PMMA showed superhydrophobic properties for metal substrate, while Si showed hydroph
... Show MoreIn this research, the geotechnical properties of the soil profile in Hilla city within Babylon Governorate in the middle parts of Iraq are described. The geotechnical data at the specific sites were collected from some geotechnical investigation reports performed at some selected locations. This article is devoted to studying the distribution of soil properties (the physical and mechanical) in the horizontal and vertical directions. Moreover, a correlation between different physical and mechanical properties is performed. The correlation is executed using statistical analysis by Microsoft Excel Software (2016). From the regression results, it was found that the nature of the soil is c